PROOF.--There, I'm down in two. But we won't rub it in. Do you notice
anything odd about these triangles? No? Well, the fact is that AD is
equal to AC, and the result of that is that the angle ACD is equal to
the angle ADC. That's Prop. 5. Anyhow, it's obvious, isn't it?
But steady on. The angle BCD is greater than its part, the angle
ACD--you must admit that? (Look out, there's a fellow going to drive.)
And therefore the angle BCD--Oh, well, I can't go into it all now or
it will mean we shall have to let these people through; but if you
carry on on those lines you'll find that BD is greater than BC.
I mean you've only got to go back to where you played your third and
you'll see that it _must_ be so, won't you? Very well, then, don't
argue.
But BD is equal to BA and AC, for AD is equal to AC; it _had_ to be,
you remember.
Therefore--now follow this closely--the two sides BA and AC are
together greater than the third side BC.
That means, you see, that by pulling your drive out to the left there
you gave yourself a lot of extra distance to cover.
You'd never have guessed that, would you? But old EUCLID did.
Come along, then; they're putting. You must be more careful at this
hole.